Abstract Mostly motivated by the crop field classification problem and the automated computational methodology for the extraction of agricultural fields with a uniform crop distribution from satellite data, we propose an indirect approach for the image segmentation which is based on the concept of a piecewise constant approximation of the slope-based vegetation indices. We discuss in detail the consistency of the new statement of segmentation problem and its solvability. We mainly focus on the rigor mathematical substantiation of the proposed approach, deriving the corresponding optimality conditions, and we show that the new optimization problem is rather a flexible and powerful model of variational image segmentation problems. We illustrate the efficiency of the proposed algorithm by numerical experiences with images that have been delivered by satellite Sentinel-2.

中文翻译：

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基于选择性平滑目标映射的分段常数逼近的卫星图像分割

摘要 主要受作物田地分类问题和从卫星数据中提取具有均匀作物分布的农田的自动化计算方法的启发，我们提出了一种基于分段常数近似概念的图像分割间接方法。基于坡度的植被指数。我们详细讨论了分割问题新陈述的一致性及其可解性。我们主要关注所提出方法的严格数学证明，推导出相应的最优条件，我们表明新的优化问题是一个灵活而强大的变分图像分割问题模型。